Notes from numbers I looked up a while ago…
For more of the notes see http://www.scribd.com/doc/38915649/Micro-Environment-Subsistence-System-Sustainable-Civilization
Assume incoming solar, when 90 degrees to the receiving surface, is about 1 kw.
Plants have limits on their rate of converting light to stored energy. Remember that plant biological processes continue at night, and that this uses up some of the energy accumulated in the presence of light. I've read that the overall theoretical efficiency of photosynthesis may be 4.5%. At 6 hour exposure, and if you could eat the entire plant, this would be an area 9 feet on a side. I've no idea what the crop would be, but you would probably be able to watch it grow…
In various sources I find that overall photosynthesis efficiency in open nature and for typical food crops (corn,wheat,rice) is .1% to .2%. For 1/10% efficiency, each of us requires 21,600 sq. ft. /hours per day. With an average of 6 hours solar exposure per day this requires a fully productive food crop area of 3,600 sq. ft., 1,800 for 2/10% This is an area much less than the 1/4 acre per person typically available for manual farming (see information on farming in Cuba post-USSR), yet higher than the 1,000 sq. ft. information from Ecology Action. More (concentrated) sun is not the answer. C3 crops (wheat, barley rice, sugar beet, potatoes) all have FALLING conversion efficiency rates as light intensity goes above 20% of full sunlight.
Potato efficiency goes up to .4%, so with 6 hours exposure you need a minimum of 900 sq. ft. In various places, I've read the most "efficient" crop is claimed to be spirulina, with production of between 5 and 15 gram per sq. yd. per day. If each gram is around 5 calories, we get somewhere between 243 ft. sq. to 720 ft. sq. per person. At the upper level of production, is we're still assuming an average of 6 hours good sun exposure, we're looking at just under 2% efficiency on converting sunlight to food energy.
While I do not really expect to find a more efficient crop than algae, perhaps hydroponic or aeroponic methods can bring up the efficiency of more traditional foods. For those with a sweet tooth, Sugar cane (a C4 crop) comes in at a yearly average of 1%, requiring 360 sq. ft. with 6 hours sunlight, and with crops such as corn and sorghum can utilize higher sun intensity.